Probabilistic fatigue methodology for six nines reliability

Fleet readiness and flight safety strongly depend on the degree of reliability that can be designed into rotorcraft flight critical components. The current U.S. Army fatigue life specification for new rotorcraft is the so-called six nines reliability, or a probability of failure of one in a million. The progress of a round robin which was established by the American Helicopter Society (AHS) Subcommittee for Fatigue and Damage Tolerance is reviewed to investigate reliability-based fatigue methodology. The participants in this cooperative effort are in the U.S. Army Aviation Systems Command (AVSCOM) and the rotorcraft industry. One phase of the joint activity examined fatigue reliability under uniquely defined conditions for which only one answer was correct. The other phases were set up to learn how the different industry methods in defining fatigue strength affected the mean fatigue life and reliability calculations. Hence, constant amplitude and spectrum fatigue test data were provided so that each participant could perform their standard fatigue life analysis. As a result of this round robin, the probabilistic logic which includes both fatigue strength and spectrum loading variability in developing a consistant reliability analysis was established. In this first study, the reliability analysis was limited to the linear cumulative damage approach. However, it is expected that superior fatigue life prediction methods will ultimately be developed through this open AHS forum. To that end, these preliminary results were useful in identifying some topics for additional study

Fractal Analysis of Protein Potential Energy Landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent \gamma, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.Comment: 17 pages, single spaced, including 12 figure

Multiphoton Absorption of Myoglobin–Nitric Oxide Complex: Relaxation by D-NEMD of a Stationary State

ABSTRACT: The photodissociation and geminate recombination of nitric oxide in myoglobin, under continuous illumination, is modeled computationally. The relaxation of the photon energy into the protein matrix is also considered in a single simulation scheme that mimics a complete experimental setup. The dynamic approach to non-equilibrium molecular dynamics is used, starting from a steady state, to compute its relaxation to equilibrium. Simulations are conducted for the native form of sperm whale myoglobin and for two other mutants, V68W and L29F, illustrating a fair diversity of spatial and temporal geminate recombination processes. Energy flow to the heme and immediate protein environment provide hints to allostery. In particular, a pathway of energy flow between the heme and the FG loop is illustrated. Although the simulations were conducted for myoglobin only, the thermal fluctuations of the FG corner are in agreement with the large structural shifts of FG during the allosteric transition of tetrameric hemoglobin

Action-derived molecular dynamics in the study of rare events

We present a practical method to generate classical trajectories with fixed initial and final boundary conditions. Our method is based on the minimization of a suitably defined discretized action. The method finds its most natural application in the study of rare events. Its capabilities are illustrated by non-trivial examples. The algorithm lends itself to straightforward parallelization, and when combined with molecular dynamics (MD) it promises to offer a powerful tool for the study of chemical reactions.Comment: 7 Pages, 4 Figures (3 in color), submitted to Phys. Rev. Let

Constant amplitude and post-overload fatigue crack growth behavior in PM aluminum alloy AA 8009

A recently developed, rapidly solidified, powder metallurgy, dispersion strengthened aluminum alloy, AA 8009, was fatigue tested at room temperature in lab air. Constant amplitude/constant delta kappa and single spike overload conditions were examined. High fatigue crack growth rates and low crack closure levels compared to typical ingot metallurgy aluminum alloys were observed. It was proposed that minimal crack roughness, crack path deflection, and limited slip reversibility, resulting from ultra-fine microstructure, were responsible for the relatively poor da/dN-delta kappa performance of AA 8009 as compared to that of typical IM aluminum alloys

Constraint methods for determining pathways and free energy of activated processes

Activated processes from chemical reactions up to conformational transitions of large biomolecules are hampered by barriers which are overcome only by the input of some free energy of activation. Hence, the characteristic and rate-determining barrier regions are not sufficiently sampled by usual simulation techniques. Constraints on a reaction coordinate r have turned out to be a suitable means to explore difficult pathways without changing potential function, energy or temperature. For a dense sequence of values of r, the corresponding sequence of simulations provides a pathway for the process. As only one coordinate among thousands is fixed during each simulation, the pathway essentially reflects the system's internal dynamics. From mean forces the free energy profile can be calculated to obtain reaction rates and insight in the reaction mechanism. In the last decade, theoretical tools and computing capacity have been developed to a degree where simulations give impressive qualitative insight in the processes at quantitative agreement with experiments. Here, we give an introduction to reaction pathways and coordinates, and develop the theory of free energy as the potential of mean force. We clarify the connection between mean force and constraint force which is the central quantity evaluated, and discuss the mass metric tensor correction. Well-behaved coordinates without tensor correction are considered. We discuss the theoretical background and practical implementation on the example of the reaction coordinate of targeted molecular dynamics simulation. Finally, we compare applications of constraint methods and other techniques developed for the same purpose, and discuss the limits of the approach

A Doubly Nudged Elastic Band Method for Finding Transition States

A modification of the nudged elastic band (NEB) method is presented that enables stable optimisations to be run using both the limited-memory quasi-Newton (L-BFGS) and slow-response quenched velocity Verlet (SQVV) minimisers. The performance of this new `doubly nudged' DNEB method is analysed in conjunction with both minimisers and compared with previous NEB formulations. We find that the fastest DNEB approach (DNEB/L-BFGS) can be quicker by up to two orders of magnitude. Applications to permutational rearrangements of the seven-atom Lennard-Jones cluster (LJ7) and highly cooperative rearrangements of LJ38 and LJ75 are presented. We also outline an updated algorithm for constructing complicated multi-step pathways using successive DNEB runs.Comment: 13 pages, 8 figures, 2 table

Maximum Flux Transition Paths of Conformational Change

Given two metastable states A and B of a biomolecular system, the problem is to calculate the likely paths of the transition from A to B. Such a calculation is more informative and more manageable if done for a reduced set of collective variables chosen so that paths cluster in collective variable space. The computational task becomes that of computing the "center" of such a cluster. A good way to define the center employs the concept of a committor, whose value at a point in collective variable space is the probability that a trajectory at that point will reach B before A. The committor "foliates" the transition region into a set of isocommittors. The maximum flux transition path is defined as a path that crosses each isocommittor at a point which (locally) has the highest crossing rate of distinct reactive trajectories. (This path is different from that of the MaxFlux method of Huo and Straub.) It is argued that such a path is nearer to an ideal path than others that have been proposed with the possible exception of the finite-temperature string method path. To make the calculation tractable, three approximations are introduced, yielding a path that is the solution of a nonsingular two-point boundary-value problem. For such a problem, one can construct a simple and robust algorithm. One such algorithm and its performance is discussed.Comment: 7 figure

Efficient Dynamic Importance Sampling of Rare Events in One Dimension

Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of efficiency, we compare implementations of ``Dynamic Importance Sampling'' (DIMS) methods to unbiased simulation. The best DIMS algorithms are shown to increase efficiency by factors of approximately 20 for a $5 k_B T$ barrier height and 300 for $9 k_B T$, compared to unbiased simulation. The gains result from close emulation of natural (unbiased), instanton-like crossing events with artificially decreased waiting times between events that are corrected for in rate calculations. The artificial crossing events are generated using the closed-form solution to the most probable crossing event described by the Onsager-Machlup action. While the best biasing methods require the second derivative of the potential (resulting from the ``Jacobian'' term in the action, which is discussed at length), algorithms employing solely the first derivative do nearly as well. We discuss the importance of one-dimensional models to larger systems, and suggest extensions to higher-dimensional systems.Comment: version to be published in Phys. Rev.

Modeling study on the validity of a possibly simplified representation of proteins

The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a good foldability and fold to the same native structure of their optimized original ones. A large ground state gap for the native structure shows the thermodynamic stability of the reduced sequences. The general validity of such a five-letter reduction is further studied via the correlation between the reduced sequences and the original ones. As a comparison, a reduction with two letters is found not to reproduce the native structure of the original sequences due to its homopolymeric features.Comment: 6 pages with 4 figure